# A Model of Room Rentals in a Seasonal Hotel Illustrating Monopolistic Competition

Author：Gerald Aranoff

A short article about my paper: “A Model of Room Rentals in a Seasonal Hotel Illustrating Monopolistic Competition” published in Theoretical Economics Letters Volume 4 number 2, pages 139-145 by Gerald Aranoff. July 9, 2014

We illustrate monopolist competition with an original theoretical model of hotel rooms available for rent on a daily basis. The product is differentiated in that hotel rooms offered for daily rental differ in location, physical aspects and service.   We assume fluctuating demand, with a peak  season, for almost two months,  and an off-peak  season, for the balance of the year.  We assume hotels set two prices, one for the peak season and one for the off-peak season. We assume no price collusion among hotels. We assume hotels know the consumer-demand schedules for their room rentals. We assume zero expected profits for all hotels in long-run equilibrium.  Initially we assume SRMC (short-run marginal-cost) pricing.

We make rigid assumptions, formulate propositions, and mathematically prove them. Our conclusions are entirely dependent on our assumptions, which allow for the mathematics, but leave open the question if realistic.

The Supply Side Assumptions:

1. We assume a single homogeneous product, hotel rooms rented at a daily rate.
2.  We assume ease of entry of new hotels.
3.  We assume two states of demand, off-peak and peak, each with a likelihood, where the likelihoods add to one.
4. There are two types of hotels, hotelK and hotelL.
5. Hotels have durable and specific assets, and linear short-run total-cost curves with absolute capacity limits.   Per-room per-day variable-operating cost, per-room per-day capacity costs (fixed costs per month divided by maximum rooms available rate per month) and capacity per hotel (maximum rooms available).
6. We envision investors and managers walking into a hotel construction store that has two shelves: each with a model hotel that costs, say, \$1,000,000 to build.  On one shelf is a model of hotelK and on the other shelf is a model hotelL.
7. Investors or entrepreneurs can order any multiple or fraction of the model hotel.
8. No economies of scale exist for hotels.
9. We assume SRMC pricing.

We show that for hotelK and hotelL to co-exist in long run equilibrium:

1. The per-room per-day variable-operating cost of hotelK must be lower than for hotelL.
2. The per-room per-day capacity costs cost of hotelK must be higher than for hotelL.
3. The capacity of the model at the hotel construction store of hotelmust be lower than for hotelL.
4. Hotelwill operate at capacity at both peak and off-peak times while hotelL will operate at capacity at peak times and shut down in off-peak time.

The conditions for hotelK and hotelL to co-exist in long run equilibrium are that hotelK is static efficient, has a lower SRACMIN, while hotelis output-rate flexible, can handle variations in output rates easily.

If demand for hotel rooms were static with no irregularities, then firms would choose only hotelK. Demand for hotel rooms is irregular in the model, fluctuating between  off-peak and peak. The added cost of supplying irregular demand in the model  is borne entirely by hotelL.

The Demand Side Assumptions

1. There are two groups in our hypothetical society: Suppliers (owners-managers of hotels) and consumers (households who rent hotel rooms).

2.  Consumers rent rooms in a free market on a daily basis from various hotels where each hotel posts its prices.

3. Consumers have a fixed budget for room rentals expenditures.

4. They are price sensitive in renting rooms, in the sense that consumers will rent more rooms at a lower market price and less rooms at a higher market price.

Proposition

We prove in the proposition that consumer surplus is necessarily larger in an arrangement where consumers get more rooms for the peak period at the cost of less rooms for the off-peak periods whereby  consumers pay the same amount  and rent the same number of rooms over the year.

We assume that suppliers are willing to offer rooms daily according to two alternative pricing schemes:  a fixed price, at all times, versus P1 for off-peak periods and P2 for the peak period.  We have two basic assumptions in the model: according to both pricing schemes total payments over the cycle are the same and total room rentals are the same.

We prove that a comparison of alternative pricing schemes, varying prices, versus a fixed price, under conditions of shifting downward-sloping demand curves shows higher consumer surplus to the fixed price arrangement which rises further as demand elasticity rises.

What may be surprising is that in the model of the paper consumers have a huge willingness to pay to get suppliers to switch from SRMC pricing to a fixed-year around price with the cost to provide for accentuated fluctuations small borne entirely by the more output-rate flexible hotelL.

Consumers have a huge willingness to pay, in the model of the paper, for the hotels to switch from SRMC pricing to a fixed price, because the consumers will be renting more rooms in the season, when their demand is high.  Making the peak season better, adds considerably to consumer welfare.  The cost of renting fewer rooms in the off-peak is of less importance.

This is an important lesson—for regularly recurring cycles—because it urges focus, even in the off-peak periods, on making the peak periods better.  This agrees with business cycle theories that urge social focus on increasing and prolonging cyclical peaks.  This supports John M. Clark’s workable competition thesis.

## Source:

Journal： Theoretical Economics Letters
DOI: 10.4236/tel.2014.42021 (PDF)
Paper Id: 43525 (metadata)